_Aliter_. Fiat PZ = √ 2 APM. & ſit ZO curvæ AZK perpendi-
cularis; erit PM = PO.

_Exemp_. Sit AP = x; & APM = {x 3 /r}. quare PZ = √ {2 x 3 /r}
unde reperietur PO = {3 x x/r} = PM; & rurſus AMB
erit _Parabola_.

## 65._Probl_. VIII.

Sit figura quævis ADB (rectis DA, DB, & linea AMB com-
prehenſa) & à Dutcunque projectâ rectâ DM, datum ſit ſpatium
ADM; oportet rectam DM definire.

### 65.1.

Fig. 190.

Acceptâ quâpiam R, ſit DZ = {2 ADM/R}; & ZO curvæ AZK
perpendicularis; cui occurrat DH ad DM perpendicularis; erit DM = √ R x DO.

_Aliter_. Sit DZ = √ 4 ADM; & ZO curvæ AZK perpen-
dicularis; cui occurrat DH ad DZ perpendicularis; erit DM
= √ DZ x DO.

_De figuris involutis & evolutis_ bellam σκέψιγ inſtituit _Præclarus Ge-_
_ometra D. Gregorius Aberd._ Alienæ meſſi nollem ego falcem meam
immittere, verùm liceat utcunque iſthuc pertinentes (aliud agenti quæ
mihi ſe ingeſſerunt) unam aut alteram obſervatiunculam his intexere.

## 66._Probl_. IX.

Data fit figura quæpiam ADB (cujus _axis_ AD, _baſis_ DB) oper-
tet ei congruentem involutam exhibere.

### 66.1.

Fig. 191.

_Centro_ C, intervallo quopiam CL deſcribatur _Circulus_ LXX; ſit
autem curva KZZ talis, ut pro lubitu ductâ rectâ MPZ ad BD pa-